Date: Mar 21, 2013 6:36 AM
Author: William Hughes
Subject: Re: Matheology § 224
On Mar 21, 11:21 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 21 Mrz., 08:57, William Hughes <wpihug...@gmail.com> wrote:
> > There is such a thing as a sufficient set of
> > lines (all sufficient sets are composed
> > entirely of unnecessary lines, which means
> > that you can remove any finite set of lines
> Why only finite sets?
You can only use induction to prove
stuff about finite sets.
> What property is changed if infinitely many are
> there? If there are infinitely many unnecessary lines, they all can be
> removed - by their property of being unnecessary.
Nope, their property of being unnecessary means
that *any one* line can be removed.
Once we remove one line, we are left with
a new set of unnecessary lines. We can
remove one of these lines.
From induction we get that
any finite set of lines can